Out of plane equilibrium points in the photogravitational elliptic restricted three body problem with oblateness up to zonal harmonics J4

The influence of the zonal harmonics J 4 on the positions and stability of the out-of-plane equilibrium points of an infinitesimal mass, in the framework of the photogravitational elliptic restricted three-body problem (ER3BP), has been investigated. The positions change with an increase in the oblateness up to zonal harmonics J 4 , radiation pressure, eccentricity and semi-major axis of the orbit. The positions and stability of the out-of-plane points are affected by the parameters involved. The effect of these parameters on the positions of the out-of-plane equilibrium points is examined numerically both for the binary system 61 CYGNI and for arbitrary values. The results obtained from this study can be applied to different methods of celestial mechanics, with application to the planetary system.